On tetravalent normal edge-transitive Cayley graphs on the modular group

A Cayley graph Gamma = Cay (G; S) on a group G with respective to a subset S subset of G, S = S-1; 1 is not an element of S, is said to be normal edge-transitive if N-Aut ((Gamma)) (rho (G)) is transitive on edges of Gamma, where rho(G) is a subgroup of Aut (Gamma) isomorphic to G. We determine all connected tetravalent normal edge-transitive Cayley graphs on the modular group of order 8n in the case that every element of S is of order 4n.